2. Let a = {vi, ... , vin} be a finite ordered basis for V. For i define fi : V —> F by Maivi ± • • • + anvn) = ai. Then 0 { fl, ... , fn} is a basis for the vector space £(V, F) (you don't need to...

2. Let a = {vi, ... , vin} be a finite ordered basis for V. For i define fi : V —> F by
Maivi ± • • • + anvn) = ai.
Then 0 { fl, ... , fn} is a basis for the vector space £(V, F) (you don't need to prove this). Let T : V —> V be a linear operator. Prove that
[T*10 ( [Tiarr)
(the transpose of the matrix [T]a.)